# Calculating long run equilibrium price and output level

Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by following linear demand function:

P= 200-QA-QB

Where QA and QB are quantities sold by the respective firms and P is the selling price. Total costs functions for the two companies are

TCA = 1,500 + 55QA +Q2A

TCB= 1,200+20QB +2Q2B

Assume that the firms act independently as in cournot model (i.e., each firm assumes that the other firm's output will not change)

a. Determine the long-run equilibrium output and selling price for each firm

b. Determine firm A, Firm B, and total industry profits at the equilibrium solution found in Part (a).

https://brainmass.com/economics/general-equilibrium/calculating-long-run-equilibrium-price-and-output-level-402193

#### Solution Preview

a. Determine the long-run equilibrium output and selling price for each firm.

In cournot competition firms compete in quantities and tend to maximize their profit

P=200-QA-QB

In case of company A

Total Revenue =TRA=P*QA=(200-QA-QB)*QA=200QA-QA^2-QAQB

Marginal Revenue=MRA=d(TRA)/dQA=200-2QA-QB

TCA=1500+55QA+QA^2

Marginal ...

#### Solution Summary

This solution describes the steps to calculate long run equilibrium output and selling price for each of the given firms. It also calculates total industry profits.